C₂₃×#1504 #15669123

order	2944
nilpotency class	3
isoclinism	isoclinic class of #1504
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₃×#1504

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
prime radical	C₂₃×#525	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂³×C₄×C₂₃ ◁ G

334 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 368

A minimal faithful permutation representation — 3 generators on 39 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(25,29,31,38)(26,33)(30,37,32,34)(35,39);(24,25)(26,34)(27,30)(28,32)(29,35)(31,36)(33,38)(37,39);(25,30)(29,37)(31,32)(34,38)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#8346, C₂₃×#8347, C₂₃×#8453, …
maximal normal subgroup of	C₂₃×#8346, C₂₃×#8347, C₂₃×#8453, …
maximal quotient of	C₂₃×#7578, C₂₃×#7579, C₂₃×#7586, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 236);